CN108375416A - A kind of Duffing oscillator detection methods of strong noise background lower linear FM signal - Google Patents
A kind of Duffing oscillator detection methods of strong noise background lower linear FM signal Download PDFInfo
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Abstract
The invention discloses a kind of Duffing oscillator detection methods of strong noise background lower linear FM signal, its main feature is that include intercepting and capturing to linear FM signal and JieDuHuaYu II Decoction, Duffing oscillator phases based on Poincare mappings characteristics functions quantitative identification and the frequency conversion Duffing oscillators of linear FM signal are detected.When being detected using this method, by changing forced frequency built in Duffing oscillator systems, scan the simple signal component in JieDuHuaYu II Decoction signal, whether the Poincare mappings characteristics functional value judgement systems exported according to detecting system resonate, and realize the LFM Signal Detection under low signal to noise ratio background.It is reasonable with methodological science, the advantages that strong applicability, effect is good.
Description
Technical field
The invention belongs to Weak Signal Detection field, it is related to a kind of strong noise background lower linear FM signal
Duffing oscillator detection methods.
Background technology
Linear FM signal is normally used as the transmitting signal of radar and active sonar detecting underwater object, due in engineering
To the needs of transmission signal parameters resolving power, linear FM signal is typically the pulse compression signal with big time width-bandwidth product.
When transmission power is certain, the frequency spectrum for emitting signal realizes extension by frequency modulating technology.By Parseval theorems it is found that frequency spectrum expands
Exhibition makes power spectrum density decline.Simultaneously as strong jamming factor exists in target scattering characteristics, external environment, usually
Make through target scattering or be reflected back receiver linear frequency modulation target echo signal it is very faint.Traditional correlation and matched filtering inspection
Survey method be using receive signal in target echo signal with transmitting signal have strong correlation, and with the incoherent property of noise
Realize Detection and Parameter Estimation.When the interference or stronger superimposed noise being subject to, detectability, which seriously sharpens, even to fail.It is common
Time-Frequency Analysis Method, Short Time Fourier Transform (STFT), wavelet transformation (WT) and Eugene Wigner-Weir distribution (WVD) etc.
Method is to be detected analysis using the time-frequency locality docking collection of letters number of kernel function.But the kernel function time-frequency of STFT is differentiated
Rate is fixed, and can not be adaptively adjusted time and frequency parameter to track signal, be analyzed the sophisticated signal effect with multi -components ingredient not
It is good.Compared with STFT, WT has adjustable time frequency resolution.But the selection of wavelet basis function is different, analytical effect is different,
And wavelet basis chooses the unified standard of neither one.WVD Time-Frequency Analysis Methods based on quadratic form are in analysis multicomponent data processing
When be inevitably present cross term, cross term, which generates interference, makes False Rate increase.Linear adjust is detected using signal decomposition theory
The main method of frequency signal includes：Blind source separating method, sparse decomposition method, Empirical mode decomposition and Independent component analysis etc..
Blind source separating method and Independent component analysis are that linear FM signal is considered as different sources from background interference, uncorrelated using its
Characteristic is detached.But when interference has certain correlation with linear FM signal, separating effect is bad.Sparse decomposition
Method is by selecting over-complete dictionary of atoms as basic function, the problem of carrying out Projective decomposition to signal, cross term interference is not present.
But since the basic function in over-complete dictionary of atoms no longer has orthogonality and uniqueness, signal point when choosing different atoms
Solution ingredient is not unique, and physical significance is indefinite.Empirical mode decomposition is incited somebody to action on the basis of defining Intrinsic mode function (IMF)
Complicated multicomponent data processing is adaptively decomposed into the form of the sum of several IMF components and residual components.When interference signal with
For linear FM signal there are when frequency overlapping interval, discomposing effect is bad.Also, there is also cross envelope, owe in decomposable process
Envelope, mode are obscured and the problems such as end effects.
In conclusion when the noise for receiving signal is relatively low, and linear frequency modulation target echo signal and noise jamming when
Domain, frequency domain and time-frequency domain have it is overlapping in the case of, above-mentioned several method separation or feature extraction are ineffective.And with typical non-thread
Property kinetic characteristics Duffing oscillator systems, do not influenced by time domain, frequency domain and Parameters of Time-frequency Field, have stronger noise exempt from
Epidemic disease characteristic still has preferable Testing of Feeble Signals ability in low signal-to-noise ratio.It is existing to detect linear adjust using Duffing oscillators
The main method of frequency signal has two classes：When by linear FM signal carry out short time treatment after, it is believed that interception when window in believe
Number frequency is steady constant, is then detected using the method that Duffing oscillator systems detect simple signal, finally by
Recognition result reconstructs time-frequency variation diagram.This method is to interfere feelings in noiseless to the detection of linear FM signal and Frequency Estimation
It is realized under condition, does not consider influence of the noise to detection performance.Second is that by linear FM signal JieDuHuaYu II Decoction, then construct
Duffing oscillator filter arrays differentiate that signal whether there is using Lyapunov indexes, and carry out parameter Estimation.This method
The phase method of discrimination of middle system selects Lyapunov index methods, complicated, and algorithm takes, and the signal-to-noise ratio of analyzed signal
Threshold value must not be less than -10dB.
Invention content
The purpose of the present invention is：Assembled with higher time-frequency using best score rank Fourier transform pairs linear FM signal
Property, it intercepts and captures the effective linear frequency modulation echo-signal received in signal and carries out JieDuHuaYu II Decoction processing, the demodulation of linear FM signal
This unknown problem of simple signal frequency obtained after frequency, the present invention provide a kind of scientific and reasonable, strong applicability, good strong of effect
The Duffing oscillator detection methods of noise background lower linear FM signal, when being detected using this method, by changing Duffing
Forced frequency built in oscillator system scans the simple signal component in JieDuHuaYu II Decoction signal, according to detecting system output
Whether Poincare mappings characteristics functional value judgement systems resonate, and realize the linear FM signal inspection under low signal to noise ratio background
It surveys.The purpose of the present invention is what is realized by following technical scheme：A kind of Duffing of strong noise background lower linear FM signal
Oscillator detection method, characterized in that it include in have：
1) to the intercepting and capturing of linear FM signal and JieDuHuaYu II Decoction
Kurtosis parameter is composed by introducing best score rank Fourier transform domain, can be prejudged out effectively from receiving in signal
LFM Echo signal data carries out next step analyzing processing, for the best score rank of effective LFM Echo signal
Fourier transform domain spectrum carries out inverse Fourier transform and realizes JieDuHuaYu II Decoction, i.e., linear FM signal is demodulated into simple signal, then
The advantage of simple signal under strong background noise is detected using Duffing oscillators, realizes the linear frequency modulation letter in the case of low signal-to-noise ratio
Number detection；
2) quantitative identification of the Duffing oscillator phases based on Poincare mappings characteristics functions
When to solve to differentiate Duffing oscillator phases using Phase Diagram Method existing subjectivity it is strong and can not automatic identification ask
Topic introduces Poincare mappings characteristics function parameters, and chaos state and the Poincare mappings of great scale period state are according to system
The otherness of characteristic function value realizes identification of the Duffing oscillator systems from chaos state to great scale period state；
3) the frequency conversion Duffing oscillators of linear FM signal are detected
By the frequency of driving force built in adjust automatically frequency conversion Duffing oscillator detecting systems, automatically scans and identify
Receive the weak linear FM signal in signal.
Further, described to include to the intercepting and capturing of linear FM signal and JieDuHuaYu II Decoction：
Transmitting amplitude is A, original frequency f0, linear FM signal that frequency modulation rate is k, expression formula is：
S (t)=Aexp (j2 π f0t+jπkt2) (1)
If it includes N number of scattered signal to receive signal, it is represented by：
Wherein, AiFor the amplitude of i-th of scattered signal, τiFor the time delay of i-th of scattered signal,For i-th of scattered signal
Phase factor；
In optimal rotation angle α=arccot (- k), best score rank Fourier transformation is：
Wherein,The best score rank Fourier transform domain spectrum for receiving signal shows as multiple impulse letters
The form of the sum of number, by δ Functional Qualities it is found that and if only if u=(f0-kτi) sin α when, Xα(u) significant, then：
It enablesFormula (4) is substituted into obtain：
It introduces best score rank Fourier transform domain and composes kurtosis parameter：
S2nX(u) it is Xα(u) 2n ranks compose instantaneous square, C4X(u) it is Xα(u) fourth order cumulant, expression formula are：
The Higher Order Cumulants of nongausian process show non-zero feature, and signal impulse when more than or equal to quadravalence
Property, non-Gaussian system are stronger, and the value of cumulant is bigger；
By theory analysis and experiment it is found that noise and the best score rank Fourier transform domain of interference compose kurtosis value in difference
The variation of time slice section is little, and the best score rank Fourier transform domain of linear FM signal spectrum kurtosis value than noise and is done
The spectrum kurtosis value disturbed is much higher.Therefore, it is composed on best score rank Fourier transform domain with linear FM signal using noise high and steep
The otherness of degree, the parameter discriminant criterion that can be intercepted and captured as strong noise background lower linear FM signal；
Fourier inversion is carried out to formula (5), that is, realizes the JieDuHuaYu II Decoction of linear FM signal：
After arrangement：
By formula (9) it is found that linear FM signal carries out the line that the time-domain signal after JieDuHuaYu II Decoction transformation is multiple simple signals
Property superposition, to the in i simple signal, frequency and amplitude are respectively fi=(f0-kτi)/csc α, Ai=Bi/ csc α, single-frequency letter
Number amount is consistent with the quantity of scattered signal, frequency fiWith time delay factor τiAnd optimal rotation angle α is related；
Further, the quantitative identification of the Duffing oscillator phases based on Poincare mappings characteristics functions
If Duffing oscillator system models are：
x″+kωx′+ω2(-x+x3)=ω2rcosωt (10)
Wherein, k is damping ratio ,-x+x3For nonlinear resilience item, rcos (ω t) is driving force built in system, and ω is interior
The angular frequency of driving force is set,
θ (θ=ω t) variable is introduced, becomes three-dimensional autonomous system after system dimensionality reduction, phase space is extended to R2×S1：
By system output Z (t)=[x (t) y (t) θ (t)]T, it is reconstructed, is obtained using the method for construction Poincare section
3 × m n dimensional vector n matrixes of one time delay：
D (t)=[Z (t), Z (t-T), Z (t-2T) ..., Z (t- (m-1) T)] (3)
Wherein, T be the driving force period built in system, m be matrix dimension, when choose section ∑=(x, y, θ) | θ=
φ }, wherein 0≤φ ＜, 2 π, write down Z (t) tracks and all intersection point d (t) in the section={ (x (tn),y(tn) | θ=φ }, n=0,
1,2,3, tnFor the time that Z (t) intersects with section { θ=φ } n-th, system output passes through delay reconstruction and the sections Poincare
The movement continuous at any time that motive power system is determined is changed into and is cut in Poincare by the Poincare mappings obtained after cutting
Discrete mapping on face, when system is in great scale period state and chaos state, the non-stationary and oscillation journey of Poincare mappings
Degree is different, and the Poincare mappings of great scale period state show as fixed point or under influence of noise by small centered on fixed point
Oscillation characteristics by a small margin in neighborhood；And the Poincare mappings of chaos state show as the Brownian movement feature of random fluctuation,
The difference of chaos state and Poincare mappings when great scale period state is according to system, structure one can quantificational description system phase
The metric parameter Poincare mappings characteristics functions of state：
Wherein, diFor the Poincare sequences of mapping of system output, N is sequence length, and α is characterized index；
When system is in great scale period state and chaos state, the non-stationary and degree of oscillation of Poincare mappings is different,
The Poincare mappings of great scale period state show as fixed point or under influence of noise in small neighbourhood centered on fixed point
The Poincare mappings characteristics functional values of oscillation characteristics by a small margin, system output are smaller；And the Poincare mapping tables of chaos state
It is now the Brownian movement feature of random fluctuation, the Poincare mappings characteristics functional values of system output are larger, therefore, can incite somebody to action
It is as from chaos state to the index parameter of great scale period state transition.
Further, the frequency conversion Duffing oscillators to linear FM signal detect
Frequency conversion Duffing oscillators detect mathematical model：
x″+ωkx′+ω2(-x+x3)=ω2(rcos(ω0t+Δωt)+s(t)) (14)
Wherein：K is system damping ratio ,-x+x3For nonlinear resilience item, rcos (ω0T+ Δs ω t) it is week built in system
Phase driving force, r are built-in driving force amplitude, ω0Built-in driving force angular frequency initial value, Δ ω are to change built-in forced frequency
Step-length；S (t) is additional driving force,
Signal s (t) is generally detected as by several simple signal components and all kinds of interference nJ(t) it is constituted with noise n (t),
Expression formula is：
Work as ω0+ Δ ω=ωiAnd r+Ai＞ rdWhen (rdFor chaos critical value), Duffing oscillator systems are to input signal
Response reaches optimal period resonance condition, and system occurs phase transition, realizes the detection of simple signal, driving force built in system
Frequency is the frequency values of simple signal.
A kind of Duffing oscillator detection methods of strong noise background lower linear FM signal of the present invention utilize best point
Number rank Fourier transform pairs linear FM signal has higher time-frequency locality, intercepts and captures the effective linear frequency modulation received in signal and returns
Wave signal simultaneously carries out JieDuHuaYu II Decoction processing, and unknown this of simple signal frequency obtained after linear FM signal JieDuHuaYu II Decoction is asked
Topic scans the simple signal component in JieDuHuaYu II Decoction signal by forced frequency built in change Duffing oscillator systems, according to
Whether the Poincare mappings characteristics functional value judgement systems of detecting system output resonate, and realize under low signal to noise ratio background
LFM Signal Detection；Kurtosis value, which is composed, according to best score rank Fourier transform domain has preselected effective number in receiving signal
It is believed that breath, after Fourier inversion JieDuHuaYu II Decoction, through frequency conversion Duffing oscillator detecting system Scanning Detctions, can recognize that
For signal-to-noise ratio down to the linear FM signal of -18dB, methodological science is reasonable, strong applicability, and effect is good.
Description of the drawings
Fig. 1 is the linear FM signal intercepting and capturing schematic diagram that kurtosis is composed based on best score rank Fourier transform domain；
Fig. 2 is a kind of block diagram of the Duffing oscillator detection methods of strong noise background lower linear FM signal.
Specific implementation mode
Below with the drawings and specific embodiments, the invention will be further described.
With reference to Fig. 2, a kind of Duffing oscillator detection methods of strong noise background lower linear FM signal of the invention, packet
It includes：Intercepting and capturing and JieDuHuaYu II Decoction to linear FM signal, the Duffing oscillator phases based on Poincare mappings characteristics functions are determined
Amount differentiates and is constituted to the detection three parts of the frequency conversion Duffing oscillators of linear FM signal.
1) to the intercepting and capturing of linear FM signal and JieDuHuaYu II Decoction
Kurtosis parameter is composed by introducing best score rank Fourier transform domain, can be prejudged out effectively from receiving in signal
LFM Echo signal data carries out next step analyzing processing, and carrying out FRFT inverse transformations for effective echo-signal realizes demodulation
Frequently, i.e., linear FM signal is demodulated into simple signal, then utilizes simple signal under Duffing oscillators detection strong background noise
Advantage, realize low signal-to-noise ratio in the case of LFM Signal Detection；
2) quantitative identification of the Duffing oscillator phases based on Poincare mappings characteristics functions
When to solve to differentiate Duffing oscillator phases using Phase Diagram Method existing subjectivity it is strong and can not automatic identification ask
Topic introduces Poincare mappings characteristics function parameters, and chaos state and the Poincare mappings of great scale period state are according to system
The otherness of characteristic function value realizes identification of the Duffing oscillator systems from chaos state to great scale period state；
3) the frequency conversion Duffing oscillators of linear FM signal are detected
By the frequency of driving force built in adjust automatically frequency conversion Duffing oscillator detecting systems, automatically scans and identify
Receive the weak linear FM signal in signal.
Further, described to include to the intercepting and capturing of linear FM signal and JieDuHuaYu II Decoction：
Transmitting amplitude is A, original frequency f0, linear FM signal that frequency modulation rate is k, expression formula is：
S (t)=Aexp (j2 π f0t+jπkt2) (1)
If it includes N number of scattered signal to receive signal, it is represented by：
Wherein, AiFor the amplitude of i-th of scattered signal, τiFor the time delay of i-th of scattered signal,For i-th of scattered signal
Phase factor；
In optimal rotation angle α=arccot (- k), best score rank Fourier transformation is：
Wherein,The best score rank Fourier transform domain spectrum for receiving signal shows as multiple impulse letters
The form of the sum of number, by δ Functional Qualities it is found that and if only if u=(f0-kτi) sin α when, Xα(u) significant, then：
It enablesFormula (4) is substituted into obtain：
It introduces best score rank Fourier transform domain and composes kurtosis parameter：
S2nX(u) it is Xα(u) 2n ranks compose instantaneous square, C4X(u) it is Xα(u) fourth order cumulant, expression formula are：
The Higher Order Cumulants of nongausian process show non-zero feature, and signal impulse when more than or equal to quadravalence
Property, non-Gaussian system are stronger, and the value of cumulant is bigger；
By theory analysis and experiment it is found that noise and the best score rank Fourier transform domain of interference compose kurtosis value in difference
The variation of time slice section is little, and the best score rank Fourier transform domain of linear FM signal spectrum kurtosis value than noise and is done
The spectrum kurtosis value disturbed is much higher.Therefore, it is composed on best score rank Fourier transform domain with linear FM signal using noise high and steep
The otherness of degree, the parameter discriminant criterion that can be intercepted and captured as strong noise background lower linear FM signal；
Fourier inversion is carried out to formula (5), that is, realizes the JieDuHuaYu II Decoction of linear FM signal：
After arrangement：
By formula (9) it is found that linear FM signal carries out the line that the time-domain signal after JieDuHuaYu II Decoction transformation is multiple simple signals
Property superposition, to the in i simple signal, frequency and amplitude are respectively fi=(f0-kτi)/csc α, Ai=Bi/ csc α, single-frequency letter
Number amount is consistent with the quantity of scattered signal, frequency fiWith time delay factor τiAnd optimal rotation angle α is related；
Further, the quantitative identification of the Duffing oscillator phases based on Poincare mappings characteristics functions
If Duffing oscillator system models are：
x″+kωx′+ω2(-x+x3)=ω2rcosωt (10)
Wherein, k is damping ratio ,-x+x3For nonlinear resilience item, rcos (ω t) is driving force built in system, and ω is interior
The angular frequency of driving force is set,
θ (θ=ω t) variable is introduced, becomes three-dimensional autonomous system after system dimensionality reduction, phase space is extended to R2×S1：
By system output Z (t)=[x (t) y (t) θ (t)]T, it is reconstructed, is obtained using the method for construction Poincare section
Obtain 3 × m n dimensional vector n matrixes of a time delay：
D (t)=[Z (t), Z (t-T), Z (t-2T) ..., Z (t- (m-1) T)] (3)
Wherein, T be the driving force period built in system, m be matrix dimension, when choose section ∑=(x, y, θ) | θ=
φ }, wherein 0≤φ ＜, 2 π, write down Z (t) tracks and all intersection point d (t) in the section={ (x (tn),y(tn) | θ=φ }, n=0,
1,2,3, tnFor the time that Z (t) intersects with section { θ=φ } n-th, system output passes through delay reconstruction and the sections Poincare
The movement continuous at any time that motive power system is determined is changed into and is cut in Poincare by the Poincare mappings obtained after cutting
Discrete mapping on face, when system is in great scale period state and chaos state, the non-stationary and oscillation journey of Poincare mappings
Degree is different, and the Poincare mappings of great scale period state show as fixed point or under influence of noise by small centered on fixed point
Oscillation characteristics by a small margin in neighborhood；And the Poincare mappings of chaos state show as the Brownian movement feature of random fluctuation,
The difference of chaos state and Poincare mappings when great scale period state is according to system, structure one can quantificational description system phase
The metric parameter Poincare mappings characteristics functions of state：
Wherein, diFor the Poincare sequences of mapping of system output, N is sequence length, and α is characterized index；
When system is in great scale period state and chaos state, the non-stationary and degree of oscillation of Poincare mappings is different,
The Poincare mappings of great scale period state show as fixed point or under influence of noise in small neighbourhood centered on fixed point
The Poincare mappings characteristics functional values of oscillation characteristics by a small margin, system output are smaller；And the Poincare mapping tables of chaos state
It is now the Brownian movement feature of random fluctuation, the Poincare mappings characteristics functional values of system output are larger, therefore, can incite somebody to action
It is as from chaos state to the index parameter of great scale period state transition.
Further, the frequency conversion Duffing oscillators to linear FM signal detect
Frequency conversion Duffing oscillators detect mathematical model：
x″+ωkx′+ω2(-x+x3(rcos (the ω of)=ω 20t+Δωt)+s(t)) (14)
Wherein：K is system damping ratio ,-x+x3For nonlinear resilience item, rcos (ω0T+ Δs ω t) it is week built in system
Phase driving force, r are built-in driving force amplitude, ω0Built-in driving force angular frequency initial value, Δ ω are to change built-in forced frequency
Step-length；S (t) is additional driving force,
Signal s (t) is generally detected as by several simple signal components and all kinds of interference nJ(t) it is constituted with noise n (t),
Expression formula is：
Work as ω0+ Δ ω=ωiAnd r+Ai＞ rdWhen (rdFor chaos critical value), Duffing oscillator systems are to input signal
Response reaches optimal period resonance condition, and system occurs phase transition, realizes the detection of simple signal, driving force built in system
Frequency is the frequency values of simple signal.
Referring to Fig.1, the intercepting and capturing stage of Linear Frequency Modulation signal, the docking collection of letters number plus sliding window carry out short time treatment.To protect
The integrality for demonstrate,proving intercepted data, avoids information from losing using following two measures：One is there is overlapping between segment data, it is overlapped number
According to the half grown for short time-window；The second is in extraction time block information, the number of the long half of short time-window is extended to both sides respectively
According to when preventing valid data to be in different piecewise intervals, there is detection leakage phenomenon.Rectangular window length is chosen and transmitting linear frequency modulation
Signal length is identical, and windowed data overlap length is the half of rectangular window length.Utilize the sliding rectangular window docking collection of letters number point
Section processing, matrix is constituted by segment dataWherein l is linear FM signal length.
By the prior information of linear FM signal, according to α0=arccot (- kTd/fs)(TdFor linear frequency modulation duration, fs
For sample frequency) best score rank rotation angle is acquired, and best score rank Fourier transformation is carried out to each row of data in matrix Z
Operation obtainsAnd it seeksKurtosis value Ki, by with Adaptive spectra kurtosis threshold value comparison, anticipation receive letter
Whether contain linear frequency modulation target echo signal in number, and intercepts and captures effective data information and carry out next step analysis.Wherein, adaptive
Kurtosis threshold value should be composed to be determined by (16) formula, i.e., the sum of the mean value of spectrum kurtosis and γ times of standard deviation are used as decision threshold value.
Wherein, KiKurtosis value is composed for the Fourier Transform of Fractional Order domain of the i-th segment data,For the variance of each section of spectrum kurtosis
Value, l are data sectional number, and γ is set as 2~4 as the case may be.By the kurtosis value K of every segment dataiWith decision threshold KdIt carries out
Compare, if Ki≥Kd, then extract the segment data and carry out next step analyzing processing；If Ki＜ Kd, then give up the segment data.
Frequency conversion Duffing oscillator detecting systems are established, system parameter setting k=0.5 is estimated by signal frequency after JieDuHuaYu II Decoction
Count range setting sweep interval [ω0,ωend], and set the critical amplitude r of chaosdValue.
With reference to Fig. 2, forced frequency initial value ω=ω built in Duffing oscillators is enabled0, signal after JieDuHuaYu II Decoction is sent into
Duffing oscillator detecting systems seek the Poincare of system output with Runge-Kutta solution by iterative method differential equation group
Characteristic function value ηi, by itself and given threshold value ηdCompare.If ηi＜ ηd, illustrating to receive has and driving force same frequency in signal
Simple signal exists, i.e., includes weak linear FM signal in the segment data, if ηi≥ηd, change built-in forced frequency ωi+1=
ωi+Δω.It repeats the above process, until the frequency final value end of scan, draws frequency and system Poincare mappings characteristics functions
Relation curve carries out conclusive judgement according to scanning result.
The software program of the present invention is people in the art according to automation, the establishment of information-based and computer processing technology
Technology known to member.
Claims (4)
1. a kind of Duffing oscillator detection methods of strong noise background lower linear FM signal, characterized in that the content that it includes
Have：
1) to the intercepting and capturing of linear FM signal and JieDuHuaYu II Decoction
Kurtosis parameter is composed by introducing best score rank Fourier transform domain, can be prejudged out in signal effectively linearly from receiving
Frequency modulation echo signal data carries out next step analyzing processing, for the best score rank Fourier of effective linear frequency modulation echo-signal
Transform domain spectrum carries out inverse Fourier transform and realizes JieDuHuaYu II Decoction, i.e., linear FM signal is demodulated into simple signal, then utilized
Duffing oscillators detect the advantage of simple signal under strong background noise, realize the linear FM signal inspection in the case of low signal-to-noise ratio
It surveys；
2) quantitative identification of the Duffing oscillator phases based on Poincare mappings characteristics functions
When to solve the problems, such as to differentiate Duffing oscillator phases using Phase Diagram Method existing subjectivity it is strong and can not automatic identification,
Poincare mappings characteristics function parameters are introduced, chaos state and great scale period state Poincare mappings characteristics are according to system
The otherness of functional value realizes identification of the Duffing oscillator systems from chaos state to great scale period state；
3) the frequency conversion Duffing oscillators of linear FM signal are detected
By the frequency of driving force built in adjust automatically frequency conversion Duffing oscillator detecting systems, automatically scans and identify reception
Weak linear FM signal in signal.
2. a kind of Duffing oscillator detection methods of strong noise background lower linear FM signal according to claim 1,
It is characterized in, it is described to include to the intercepting and capturing of linear FM signal and JieDuHuaYu II Decoction content：
Transmitting amplitude is A, original frequency f0, linear FM signal that frequency modulation rate is k, expression formula is：
S (t)=Aexp (j2 π f0t+j π kt2)(1)
If it includes N number of scattered signal to receive signal, it is represented by：
Wherein, AiFor the amplitude of i-th of scattered signal, τiFor the time delay of i-th of scattered signal,For the phase of i-th of scattered signal
Location factor；
In optimal rotation angle α=arccot (- k), best score rank Fourier transformation is：
Wherein,Receive signal best score rank Fourier transform domain spectrum show as multiple impulse functions it
The form of sum, by δ Functional Qualities it is found that and if only if u=(f0-kτi) sin α when, Xα(u) significant, then：
It enablesFormula (4) is substituted into obtain：
It introduces best score rank Fourier transform domain and composes kurtosis parameter：
S2nX(u) it is Xα(u) 2n ranks compose instantaneous square, C4X(u) it is Xα(u) fourth order cumulant, expression formula are：
The Higher Order Cumulants of nongausian process show non-zero feature when more than or equal to quadravalence, and signal impulse, non-
Gaussian stronger, the value of cumulant is bigger；
By theory analysis and experiment it is found that noise and the best score rank Fourier transform domain of interference compose kurtosis value in different time
Piecewise interval variation is little, and the best score rank Fourier transform domain of linear FM signal spectrum kurtosis value is than noise and interference
It is much higher to compose kurtosis value.Therefore, kurtosis is composed on best score rank Fourier transform domain using noise and linear FM signal
Otherness, the parameter discriminant criterion that can be intercepted and captured as strong noise background lower linear FM signal；
Fourier inversion is carried out to formula (5), that is, realizes the JieDuHuaYu II Decoction of linear FM signal：
After arrangement：
By formula (9) it is found that it is the linear folded of multiple simple signals that linear FM signal, which carries out the time-domain signal after JieDuHuaYu II Decoction transformation,
Add, in i simple signal, frequency and amplitude are respectively fi=(f0-kτi)/csc α, Ai=Bi/ csc α, simple signal number
Measure, frequency f consistent with the quantity of scattered signaliWith time delay factor τiAnd optimal rotation angle α is related.
3. a kind of Duffing oscillator detection methods of strong noise background lower linear FM signal according to claim 1,
It is characterized in, the quantitative identification content of the Duffing oscillator phases based on Poincare mappings characteristics functions includes：
If Duffing oscillator system models are：
x″+kωx′+ω2(-x+x3)=ω2rcosωt (10)
Wherein, k is damping ratio ,-x+x3For nonlinear resilience item, rcos (ω t) is driving force built in system, and ω is built-in plan
The angular frequency of power,
θ (θ=ω t) variable is introduced, becomes three-dimensional autonomous system after system dimensionality reduction, phase space is extended to R2×S1：
By system output Z (t)=[x (t) y (t) θ (t)]T, it is reconstructed using the method for construction Poincare section, obtains one
3 × m n dimensional vector n matrixes of time delay：
D (t)=[Z (t), Z (t-T), Z (t-2T) ..., Z (t- (m-1) T)] (3)
Wherein, T be the driving force period built in system, m be matrix dimension, when choose section ∑={ (x, y, θ) θ=φ },
In 0≤φ ＜, 2 π, write down Z (t) tracks and all intersection point d (t) in the section={ (x (tn),y(tn) | θ=φ }, n=0,1,2,3,
tnFor the time that Z (t) intersects with section { θ=φ } n-th, system output is after delay reconstruction and the cutting of the sections Poincare
The Poincare of acquisition maps, by the movement continuous at any time that motive power system is determined be changed on the sections Poincare from
Scattered mapping, when system is in great scale period state and chaos state, the non-stationary and degree of oscillation of Poincare mappings is different,
The Poincare mappings of great scale period state show as fixed point or under influence of noise in small neighbourhood centered on fixed point
Oscillation characteristics by a small margin；And the Poincare mappings of chaos state show as the Brownian movement feature of random fluctuation, according to being
The difference of Poincare mappings when system is in chaos state and great scale period state, structure one can quantificational description system phase degree
Measure parameter Poincare mappings characteristics functions：
Wherein, diFor the Poincare sequences of mapping of system output, N is sequence length, and α is characterized index；
When system is in great scale period state and chaos state, the non-stationary and degree of oscillation of Poincare mappings is different, big ruler
Degree period state Poincare mapping show as fixed point or under influence of noise in small neighbourhood centered on fixed point slightly
Oscillation characteristics are spent, the Poincare mappings characteristics functional values of system output are smaller；And the Poincare mappings of chaos state are shown as
The Brownian movement feature of random fluctuation, the Poincare mappings characteristics functional values of system output are larger, therefore, can be made
For from chaos state to the index parameter of great scale period state transition.
4. a kind of Duffing oscillator detection methods of strong noise background lower linear FM signal according to claim 1,
It is characterized in, the content of the frequency conversion Duffing oscillators detection to linear FM signal includes：
Frequency conversion Duffing oscillators detect mathematical model：
x″+ωkx′+ω2(-x+x3)=ω2(rcos(ω0t+Δωt)+s(t)) (14)
Wherein：K is system damping ratio ,-x+x3For nonlinear resilience item, rcos (ω0T+ Δs ω t) it is period plan built in system
Power, r are driving force amplitude, ω0Angular frequency initial value, Δ ω are the step-length for changing built-in forced frequency；S (t) is additional drive
Power,
Signal s (t) is generally detected as by several simple signal components and all kinds of interference nJ(t) it is constituted with noise n (t), expression formula
For：
Work as ω0+ Δ ω=ωiAnd r+Ai＞ rdWhen (rdFor chaos critical value), response of the Duffing oscillator systems to input signal
Reach optimal period resonance condition, system occurs phase transition, realizes the detection of simple signal, the frequency of driving force built in system
The as frequency values of simple signal.
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